what is the producer for the chicken in merge cooking?

The chicken in Merge Cooking: Theme Restaurant appears to come from the poultry/protein generator that produces poultry items, based on player discussions about the game’s generators and ingredient chains.

What that means

• Players refer to a protein generator that can produce poultry, and chicken is part of that category.

• In gameplay guides, chicken-related items are treated as ingredients you obtain through the game’s merging/generator system rather than by a separate “producer” with a unique name.

• If you mean a specific chicken dish or level item, the exact source can vary by recipe chain.

Quick read

So the short answer is: the chicken is produced by the protein/poultry generator.

TL;DR: In Merge Cooking, chicken is tied to the protein generator that outputs poultry items.